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Naively, I have regarded the expression sich nicht ausschließen lassen as something that one would typically apply to one hypothesis out of several (especially if this hypothesis looks particularly unlikely), and would translate it as cannot be ruled out.

In summary, I have understood the phrase as an acknowledgement of possibility that nevertheless still conveys a considerable measure of doubt.

I just came across the phrase sich nicht ausschließen lassen in a context that contradicts this understanding of it.

The original source is the book Duden Redewendungen, on p. 321:

sich nicht von der Hand weisen lassen/nicht von der Hand zu weisen sein: offenkundig, nicht zu verkennen sein, sich nicht ausschließen lassen: ...

Going only by the other alternative definitions that precede it in this citation, I would conclude that sich nicht ausschließen lassen was more or less synonymous with offenkundig [sein] ("to be obvious") and nicht zu verkennen sein ("impossible to miss, unmistakable")1.

Contrary to my original translation, these alternative translations convey the impossibility of doubt.

How is this contradiction to be resolved?

1 Implicit in this interpretation is the assumption that, in the context of a definition appearing in a work of reference, comma-separated alternatives are to be taken as "more or less synonymous".

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    In this case, IMHO, the comma-separated alternatives are only similar, i.e. more or less synonymous. The exact meaning of *nicht von der Hand zu weisen" depends on the context, and this determines which alternative fits best.
    – Bodo
    May 19, 2021 at 13:53
  • I miss some context here, but can't imagine a claim is made by Duden, that these two phrases have the same meaning. Nicht auszuschließen sein means unlikely, probability near zero, but still somewhat greater. Offenkundig sein or nicht von der Hand zu weisen sein is at the other end, i. e. practically sure.
    – guidot ♦
    May 19, 2021 at 14:33
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    Persons can also become 'ausgeschlossen', meaning they are not allowed to participate or not included in a restriction. Like in 'Anwohner ausgeschlossen', 'geschlossene Gesellschaft', 'ausschließlich Mitglieder', etc.
    – user41853
    May 19, 2021 at 16:13
  • @Bodo: Just to make sure I don't misunderstand you: are you saying that the turn of phrase nicht von der Hand zu weisen sein can mean, depending on context, either "it is obvious" or "it cannot be ruled out"? Such degree of divergence between alternative meanings would be remarkable, but, I guess, it cannot be ruled out! :D
    – kjo
    May 19, 2021 at 20:22
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    nicht von der Hand zu weisen sein means it cannot be ruled out. Depending on the context it can mean that something is unlikely but not impossible or that something is obvious. I think that this phrase simply doesn't specify the probability.
    – Bodo
    May 20, 2021 at 7:01

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The correct interpretation of "sich nicht ausschließen lassen" is definitely that something cannot be ruled out.

In your question you consider the phrase "sich nicht von der Hand weisen lassen / nicht von der Hand zu weisen sein". Duden explains it as "offenkundig, nicht zu verkennen sein, sich nicht ausschließen lassen". These are no synonyms. Duden offers a broader range of interpreting "sich nicht von der Hand weisen lassen" - from being completely obvious to deserving further consideration (depending on the context).

In my opinion you can "order by strength"

  1. offenkundig

  2. nicht von der Hand zu weisen

  3. sich nicht ausschließen lassen

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